rlx-fdm 0.2.13

Force density method (FDM) for RLX — pin-jointed form-finding ported from jax_fdm.
Documentation 
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139

// RLX — versatile ML compiler + runtime.
// Copyright (C) 2026 Eugene Hauptmann, Nataliya Kosmyna.
//
// This program is free software: you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation, version 3.
//
// This program is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU General Public License
// along with this program. If not, see <https://www.gnu.org/licenses/>.

//! Mesh structures for face tributary loads (jax_fdm `equilibrium.structures.meshes`).

use crate::network::{Network, Vec3};
use crate::structure::Structure;

/// Mesh topology layered on a pin-jointed [`Structure`].
#[derive(Clone, Debug)]
pub struct MeshStructure {
    pub base: Structure,
    /// Face vertex index lists (≥ 3 vertices each).
    pub faces: Vec<Vec<usize>>,
    /// Up to two incident face indices per edge (`None` = boundary).
    pub edges_faces: Vec<[Option<usize>; 2]>,
    /// Row-normalized face–vertex matrix flattened `[num_faces, num_nodes]`.
    pub face_vertex_weights: Vec<f64>,
}

impl MeshStructure {
    pub fn from_network_and_faces(network: &Network, faces: Vec<Vec<usize>>) -> Self {
        let base = Structure::from_network(network);
        let edges_faces = edges_faces_from_mesh(&faces, &network.edges);
        let face_vertex_weights = face_vertex_matrix(&faces, base.num_nodes);
        Self {
            base,
            faces,
            edges_faces,
            face_vertex_weights,
        }
    }

    pub fn num_faces(&self) -> usize {
        self.faces.len()
    }

    /// Face centroids `C_fv @ xyz` (jax_fdm `connectivity_faces_vertices @ xyz`).
    pub fn face_centroids(&self, xyz: &[f64]) -> Vec<Vec3> {
        let n = self.base.num_nodes;
        let nf = self.num_faces();
        let mut out = vec![0.0; nf * 3];
        for f in 0..nf {
            for v in 0..n {
                let w = self.face_vertex_weights[f * n + v];
                if w == 0.0 {
                    continue;
                }
                out[f * 3] += w * xyz[v * 3];
                out[f * 3 + 1] += w * xyz[v * 3 + 1];
                out[f * 3 + 2] += w * xyz[v * 3 + 2];
            }
        }
        (0..nf)
            .map(|f| [out[f * 3], out[f * 3 + 1], out[f * 3 + 2]])
            .collect()
    }
}

fn face_vertex_matrix(faces: &[Vec<usize>], num_nodes: usize) -> Vec<f64> {
    let nf = faces.len();
    let mut f = vec![0.0; nf * num_nodes];
    for (fi, face) in faces.iter().enumerate() {
        let valid: Vec<usize> = face.iter().copied().filter(|&v| v < num_nodes).collect();
        if valid.is_empty() {
            continue;
        }
        let inv = 1.0 / valid.len() as f64;
        for v in valid {
            f[fi * num_nodes + v] = inv;
        }
    }
    f
}

fn edges_faces_from_mesh(
    faces: &[Vec<usize>],
    edges: &[(usize, usize)],
) -> Vec<[Option<usize>; 2]> {
    let mut out = vec![[None, None]; edges.len()];
    for (fi, face) in faces.iter().enumerate() {
        let loopv: Vec<usize> = face
            .iter()
            .copied()
            .filter(|&v| v < usize::MAX / 2)
            .collect();
        if loopv.len() < 3 {
            continue;
        }
        for i in 0..loopv.len() {
            let u = loopv[i];
            let v = loopv[(i + 1) % loopv.len()];
            for (ei, &(a, b)) in edges.iter().enumerate() {
                if (a == u && b == v) || (a == v && b == u) {
                    if out[ei][0].is_none() {
                        out[ei][0] = Some(fi);
                    } else if out[ei][1].is_none() && out[ei][0] != Some(fi) {
                        out[ei][1] = Some(fi);
                    }
                }
            }
        }
    }
    out
}

/// Unique edges from face loops (jax_fdm `Mesh._edges_from_faces`).
pub fn edges_from_faces(faces: &[Vec<usize>]) -> Vec<(usize, usize)> {
    let mut half = Vec::new();
    for face in faces {
        if face.len() < 3 {
            continue;
        }
        for i in 0..face.len() {
            half.push((face[i], face[(i + 1) % face.len()]));
        }
    }
    let mut edges = Vec::new();
    let mut seen = std::collections::HashSet::new();
    for (u, v) in half {
        let key = if u < v { (u, v) } else { (v, u) };
        if seen.insert(key) {
            edges.push(key);
        }
    }
    edges
}